How do I set up a 3rd person character with multiple animations in the Game Engine?
Just use only one armature for your character.

Create your two different actions on the same armature. Make sure that no bone is used in different actions at the same time. (In your case: action one -> exclusively the upper body part, action two -> only bones of the lower half)

Last thing you have to do, is to select different Action-Layers for your actions in each action-actuator.